Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet

Numerical calculations reveal that the true ground state of a frustrated two-dimensional system is a gapped spin liquid. We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We study this model on numerous long cylinders with circumferences up to 12 lattice spacings. Through a combination of very-low-energy and small finite-size effects, our results provide strong evidence that, for the infinite two-dimensional system, the ground state of this model is a fully gapped spin liquid.

[1]  L. Balents.  Spin liquids in frustrated magnets , 2010, Nature.

[2]  D. Schwandt,et al.  Effective quantum dimer model for the kagome Heisenberg antiferromagnet: Nearby quantum critical point and hidden degeneracy , 2009, 0912.0724.

[3]  P. Sindzingre,et al.  Low-energy excitations of the kagomé antiferromagnet and the spin-gap issue , 2009, 0907.4164.

[4]  G. Evenbly,et al.  Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice. , 2009, Physical review letters.

[5]  Hong-Chen Jiang,et al.  Density matrix renormalization group numerical study of the kagome antiferromagnet. , 2008, Physical review letters.

[6]  D. Huse,et al.  Triplet and singlet excitations in the valence bond crystal phase of the kagome lattice Heisenberg model , 2008, 0801.2735.

[7]  D. Huse,et al.  Ground state of the spin-1/2 kagome-lattice Heisenberg antiferromagnet , 2007, 0707.0892.

[8]  Steven R White,et al.  Neél order in square and triangular lattice Heisenberg models. , 2007, Physical review letters.

[9]  Ying Ran,et al.  Projected-wave-function study of the spin-1/2 Heisenberg model on the Kagomé lattice. , 2006, Physical review letters.

[10]  T. Senthil,et al.  Physics of low-energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet , 2003, cond-mat/0305189.

[11]  G. Misguich,et al.  Quantum dimer model with extensive ground-state entropy on the kagome lattice , 2003, cond-mat/0302152.

[12]  R. Moessner,et al.  Resonating valence bond phase in the triangular lattice quantum dimer model. , 2000, Physical review letters.

[13]  H. Everts,et al.  First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice , 1998, cond-mat/9802168.

[14]  S. White,et al.  DENSITY MATRIX RENORMALIZATION GROUP STUDY OF THE STRIPED PHASE IN THE 2D T-J MODEL , 1998 .

[15]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[16]  White,et al.  Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S=1 Heisenberg chain. , 1993, Physical review. B, Condensed matter.

[17]  V. Elser,et al.  Numerical studies of a 36-site kagomé antiferromagnet , 1993 .

[18]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[19]  Sachdev,et al.  Kagomé- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons. , 1992, Physical review. B, Condensed matter.

[20]  Wen,et al.  Mean-field theory of spin-liquid states with finite energy gap and topological orders. , 1991, Physical review. B, Condensed matter.

[21]  J. Marston,et al.  Spin‐Peierls and spin‐liquid phases of Kagomé quantum antiferromagnets , 1991 .

[22]  Read,et al.  Large-N expansion for frustrated quantum antiferromagnets. , 1991, Physical review letters.

[23]  Read,et al.  Statistics of the excitations of the resonating-valence-bond state. , 1989, Physical review. B, Condensed matter.

[24]  Elser,et al.  Nuclear antiferromagnetism in a registered 3He solid. , 1989, Physical review letters.

[25]  J. Sethna,et al.  Topology of the resonating valence-bond state: Solitons and high-Tc superconductivity. , 1987, Physical review. B, Condensed matter.

[26]  Philip W. Anderson,et al.  Resonating valence bonds: A new kind of insulator? , 1973 .

[27]  E. Lieb,et al.  Two Soluble Models of an Antiferromagnetic Chain , 1961 .